Documentation
& Structural Hub
Technical documentation, derivation papers, and CLI reference for the BPR framework. Start with the Mathematical Spine if you're new; jump to Whitepapers if you want the derivations.
System Feed
View All Logsa₀ Derived from Gibbons-Hawking Temperature
APR 5First-principles derivation of the Bohr radius a₀ from substrate Gibbons-Hawking temperature. Closes the loop on the hydrogen energy spectrum without any atomic-scale inputs.
BPRBoundaryPhonon: p^{1/3} ΔN_eff Ceiling
APR 5New falsifiable prediction: the effective number of relativistic species ΔN_eff is bounded above by p^{1/3} ≈ 47.1, matching CMB constraints. Direct test for next-generation CMB-S4 observations.
BPR Cosmology v7: MOND-Enhanced Baryonic Retention
APR 4Added f_star channel: BPR predicts the stellar fraction f_★ from substrate impedance and MOND acceleration scale. Connects dark matter, baryogenesis, and structure formation in a single derivation chain.
Core Mathematical Spine
Interactive visualization of resonance equations. Access the raw LaTeX files and Wolfram integration modules.
Ψ(x, t) = Σ cₙ φₙ(x) e^(-iEₙt/ħ)
// Resonance Node Delta v1.2
Papers & Documents
Core BPR documents hover to download or open.
Boundary Phase Resonance: Full Mathematical Spine
13 pages · Apr 2026 · Jack Al-Kahwati
Experimental Falsification Roadmap
10 concrete tests · 2026–2030
BPR: A Mathematical Theory of Everything
228 KB · 24 theories · Jack Al-Kahwati
BPR-Math-Spine Codebase
24 theories · 87 predictions · 1,225 tests
Quickstart
Getting Started
Three ways to run BPR, in order of effort. All produce the same predictions.
Browser (0 setup)
Use this site. The constant calculator, physics landscape, and experimental roadmap all run in your browser with no installation.
Python (5 min)
Clone and run. Requires Python 3.10+. FEniCS optional most functionality works without it.
BPR-Math-Spine
Docker (full FEniCS)
Universal runs on any platform including Apple Silicon. Includes FEniCS for boundary mesh generation and all 1,225 tests.
What BPR Derives from Two Numbers (J, p)
Transparency
Peer Review Status
Honest assessment of where BPR stands. We believe open pre-publication review is more valuable than a single round of anonymous referee feedback.
What We Claim vs. Don't Claim
Global Consistency Audit
58 internal mathematical consistency tests no experiments needed. All pass.
Developer Access
API & Rate Limits
Programmatic access to BPR predictions, derivations, and parameter lookups. All tiers are free during the public research period.
Public
No key required. Good for exploration.
- 30 requests / hour
- 5 requests / minute
- Read-only endpoints
- JSON responses
curl https://api.bpr.science/v1/constants/alpha
Free Key
Request via email. Approved within 24h.
- 1,000 requests / hour
- 60 requests / minute
- All endpoints incl. batch
- CSV + JSON responses
- Full predictions CSV (205 rows)
- Python SDK access
Unlimited
For universities, labs, and research groups.
- Unlimited requests
- Priority queue
- Private derivation runs
- Webhook callbacks
- Dedicated support
Key Endpoints
| Method | Endpoint | Returns | Tier |
|---|---|---|---|
| GET | /v1/constants/{name} | Single constant + derivation | Public |
| GET | /v1/constants | All 87 constants | Public |
| GET | /v1/predictions | Full 205-row CSV / JSON | Key |
| POST | /v1/derive | Run derivation from (J,p,N) | Key |
| GET | /v1/landscape | Physics landscape graph JSON | Key |
| GET | /v1/audit/consistency | 58 consistency test results | Institution |
# Install: git clone + pip install -e .
from bpr.alpha_derivation import derive_alpha
from bpr.cross_predictions import full_cosmological_chain
from bpr import pipelines
# Derive the fine-structure constant from substrate integers
result = derive_alpha(p=104729, z=6)
print(result["alpha"], result["inv_alpha_percent_error"])
# Run 200+ predictions from (p, z)
chain = full_cosmological_chain(p=104729, z=6)
# Run a named prediction pipeline
casimir = pipelines.pipeline_substrate_to_casimir(p=104729, z=6)# Install (from repo)
pip install -e .
# Look up constants (filter by name)
bpr constants --filter alpha
# Run a named derivation pipeline
bpr pipeline casimir
# Verify field equations symbolically
bpr verify